GraphX is a graph computing library based on Spark systems,where fault tolerance is a necessary guarantee for the high availability.However,the existing fault tolerance methods are mostly implemented in a pessimistic ...GraphX is a graph computing library based on Spark systems,where fault tolerance is a necessary guarantee for the high availability.However,the existing fault tolerance methods are mostly implemented in a pessimistic way and are aimed at general computing tasks.Considering the characteristics of iterative computation,this paper presents a combination method of the optimistic fault tolerance and checkpoint for recovering the data under different failure conditions.Firstly,for single node failure,we propose the optimistic fault tolerance mechanism based on compensation function.It does not add fault tolerance measures in advance and will not incur additional costs when there are no failures.Secondly,for multiple node failures,we propose the automatic checkpoint management strategy based on RDD importance.It comprehensively considers the factors of lineage length of RDD,dependency relationship,and computation time of RDD,which can set the RDD as the checkpoint properly.Finally,we implement our proposals in GraphX of Spark−3.5.1,and evaluate the performance by using representative iterative graph algorithms on the high performance computing cluster.The results verify the correctness of iteration results of the mechanism,and illustrate that when recovering the RDD partition,the job execution time can be reduced by the mechanism and strategy substantially.展开更多
In this paper, we derive, by presenting some suitable notations, three typical graph aLgorithms and corresponding programs using a unified approach, partition-and-recur. We putemphasis on the derivation rather than th...In this paper, we derive, by presenting some suitable notations, three typical graph aLgorithms and corresponding programs using a unified approach, partition-and-recur. We putemphasis on the derivation rather than the algorithms themselves. The main ideas and lugesnutty of these algorithms are revealed by formula deduction. Success in these examples givesus more evidence that partition-and-recur is a simple and practical approach and developingenough suitable notations is the key in designing and deriving efficient and correct algorithmicprograms.展开更多
Hardware/software(HW/SW) partitioning is one of the key processes in an embedded system.It is used to determine which system components are assigned to hardware and which are processed by software.In contrast with p...Hardware/software(HW/SW) partitioning is one of the key processes in an embedded system.It is used to determine which system components are assigned to hardware and which are processed by software.In contrast with previous research that focuses on developing efficient heuristic,we focus on the pre-process of the task graph before the HW/SW partitioning in this paper,that is,enumerating all the sub-graphs that meet the requirements.Experimental results showed that the original graph can be reduced to 67% in the worst-case scenario and 58% in the best-case scenario.In conclusion,the reduced task graph saved hardware area while improving partitioning speed and accuracy.展开更多
Femtocell is a promising technology for improving indoor coverage and offloading the macrocell.Femtocells tend to be densely deployed in populated areas such as the dormitories.However,the inter-tier interference seri...Femtocell is a promising technology for improving indoor coverage and offloading the macrocell.Femtocells tend to be densely deployed in populated areas such as the dormitories.However,the inter-tier interference seriously exists in the co-channel Densely Deployed Femtocell Network(DDFN).Since the Femtocell Access Points(FAPs) are randomly deployed by their customers,the interference cannot be predicted in advance.Meanwhile,new characteristics such as the short radius of femtocell and the small number of users lead to the inefficiency of the traditional frequency reuse algorithms such as Fractional Frequency Reuse(FFR).Aiming for the downlink interference coordination in the DDFN,in this paper,we propose a User-oriented Graph based Frequency Allocation(UGFA)algorithm.Firstly,we construct the interference graph for users in the network.Secondly,we study the conventional graph based resources allocation algorithm.Then an improved two steps graph based frequency allocation mechanism is proposed.Simulation results show that UGFA has a high frequency reuse ratio mean while guarantees a better throughput.展开更多
Blockchain technology,with its attributes of decentralization,immutability,and traceability,has emerged as a powerful catalyst for enhancing traditional industries in terms of optimizing business processes.However,tra...Blockchain technology,with its attributes of decentralization,immutability,and traceability,has emerged as a powerful catalyst for enhancing traditional industries in terms of optimizing business processes.However,transaction performance and scalability has become the main challenges hindering the widespread adoption of blockchain.Due to its inability to meet the demands of high-frequency trading,blockchain cannot be adopted in many scenarios.To improve the transaction capacity,researchers have proposed some on-chain scaling technologies,including lightning networks,directed acyclic graph technology,state channels,and shardingmechanisms,inwhich sharding emerges as a potential scaling technology.Nevertheless,excessive cross-shard transactions and uneven shard workloads prevent the sharding mechanism from achieving the expected aim.This paper proposes a graphbased sharding scheme for public blockchain to efficiently balance the transaction distribution.Bymitigating crossshard transactions and evening-out workloads among shards,the scheme reduces transaction confirmation latency and enhances the transaction capacity of the blockchain.Therefore,the scheme can achieve a high-frequency transaction as well as a better blockchain scalability.Experiments results show that the scheme effectively reduces the cross-shard transaction ratio to a range of 35%-56%and significantly decreases the transaction confirmation latency to 6 s in a blockchain with no more than 25 shards.展开更多
In this paper, a new approach for visualizing multivariate categorical data is presented. The approach uses a graph to represent multivariate categorical data and draws the graph in such a way that we can identify pat...In this paper, a new approach for visualizing multivariate categorical data is presented. The approach uses a graph to represent multivariate categorical data and draws the graph in such a way that we can identify patterns, trends and relationship within the data. A mathematical model for the graph layout problem is deduced and a spectral graph drawing algorithm for visualizing multivariate categorical data is proposed. The experiments show that the drawings by the algorithm well capture the structures of multivariate categorical data and the computing speed is fast.展开更多
To construct a high efficient text clustering algorithm the multilevel graph model and the refinement algorithm used in the uncoarsening phase is discussed. The model is applied to text clustering. The performance of ...To construct a high efficient text clustering algorithm the multilevel graph model and the refinement algorithm used in the uncoarsening phase is discussed. The model is applied to text clustering. The performance of clustering algorithm has to be improved with the refinement algorithm application. The experiment result demonstrated that the multilevel graph text clustering algorithm is available. Key words text clustering - multilevel coarsen graph model - refinement algorithm - high-dimensional clustering CLC number TP301 Foundation item: Supported by the National Natural Science Foundation of China (60173051)Biography: CHEN Jian-bin(1970-), male, Associate professor, Ph. D., research direction: data mining.展开更多
Many real-world networks are found to be scale-free. However, graph partition technology, as a technology capable of parallel computing, performs poorly when scale-free graphs are provided. The reason for this is that...Many real-world networks are found to be scale-free. However, graph partition technology, as a technology capable of parallel computing, performs poorly when scale-free graphs are provided. The reason for this is that traditional partitioning algorithms are designed for random networks and regular networks, rather than for scale-free networks. Multilevel graph-partitioning algorithms are currently considered to be the state of the art and are used extensively. In this paper, we analyse the reasons why traditional multilevel graph-partitioning algorithms perform poorly and present a new multilevel graph-partitioning paradigm, top down partitioning, which derives its name from the comparison with the traditional bottom-up partitioning. A new multilevel partitioning algorithm, named betweenness-based partitioning algorithm, is also presented as an implementation of top-down partitioning paradigm. An experimental evaluation of seven different real-world scale-free networks shows that the betweenness-based partitioning algorithm significantly outperforms the existing state-of-the-art approaches.展开更多
电力系统的安全稳定运行是保障国家能源安全和经济发展的关键,而这在很大程度上依赖于对电力物联设备故障的准确预测。当前,随着电力物联网技术的发展,大量的数据被采集,但这些数据的潜在价值尚未得到充分挖掘,这在一定程度上限制了故...电力系统的安全稳定运行是保障国家能源安全和经济发展的关键,而这在很大程度上依赖于对电力物联设备故障的准确预测。当前,随着电力物联网技术的发展,大量的数据被采集,但这些数据的潜在价值尚未得到充分挖掘,这在一定程度上限制了故障预测的准确性,影响了电力系统的可靠运行。针对这一问题,该文提出了一种创新的基于GraphSAGE(Graph Sample and Aggregate)算法的电力物联设备故障预测。该方法通过PowerGraph数据集,将电力物联设备故障场景细分为四类,利用GraphSAGE模型的特性,深入学习和分析节点特征与边特征,从而实现对物联设备故障的有效预测。实验结果表明,该方法准确率达到97.5%,相较于其它传统方法,准确率提高了0.39%~6.21%,同时GraphSAGE模型实现了快速训练。该方法为电力物联设备安全稳定运行提供重要决策支持,能够对动态和相互联系的复杂系统进行更精细的分析,并增强电力系统运营部门对潜在干扰的预见和应对能力。展开更多
The 2-step domination problem is to find a minimum vertex set D of a graph such that every vertex of the graph is either in D or at distance two from some vertex of D. In the present paper, by using a labeling method,...The 2-step domination problem is to find a minimum vertex set D of a graph such that every vertex of the graph is either in D or at distance two from some vertex of D. In the present paper, by using a labeling method, we provide an O(m) time algorithm to solve the 2-step domination problem on block graphs, a superclass of trees.展开更多
It is a common practice to simulate some historical or test systems to validate the efficiency of new methods or concepts. However, there are only a small number of existing power system test cases, and validation and...It is a common practice to simulate some historical or test systems to validate the efficiency of new methods or concepts. However, there are only a small number of existing power system test cases, and validation and evaluation results, obtained using such a limited number of test cases, may not be deemed sufficient or convincing. In order to provide more available test cases, a new random graph generation algorithm, named ‘‘dualstage constructed random graph’’ algorithm, is proposed to effectively model the power grid topology. The algorithm generates a spanning tree to guarantee the connectivity of random graphs and is capable of controlling the number of lines precisely. No matter how much the average degree is,whether sparse or not, random graphs can be quickly formed to satisfy the requirements. An approach is developed to generate random graphs with prescribed numbers of connected components, in order to simulate the power grid topology under fault conditions. Our experimental study on several realistic power grid topologies proves that the proposed algorithm can quickly generate a large number of random graphs with the topology characteristics of real-world power grid.展开更多
Optical transport networks are now the basic infrastructure of modern communications systems, including the SDH and WDM backbone network of local network operators, in the case of Cameroon. Given the colossal investme...Optical transport networks are now the basic infrastructure of modern communications systems, including the SDH and WDM backbone network of local network operators, in the case of Cameroon. Given the colossal investments required to deploy these networks, particularly related to the cost of equipment (optical fibers, transponders and multiplexers), the optimization of bandwidth and dynamic allocation of resources is essential to control operating costs and ensure continuity of service. Automatic switching technology for optical networks brings intelligence to the control plane to fully facilitate bandwidth utilization, traffic redirection, and automatic configuration of end-to-end services. This paper considers a local network operator’s WDM network without the implementation of the automatic switching technology, develops a network modeling software platform called Graphic Networks and using graph theory integrates a particularity of the automatic switching technology, which is the automatic rerouting of traffic in case of incident in the network. The incidents considered here are those links or route failures and node failures.展开更多
Given n unit execution time (UET) tasks whose precedence constraints form a directed acyclic graph, the arcs are associated with unit communication time (UCT) delays. The problem is to schedule the tasks on two identi...Given n unit execution time (UET) tasks whose precedence constraints form a directed acyclic graph, the arcs are associated with unit communication time (UCT) delays. The problem is to schedule the tasks on two identical processors in order to minimize the makespan. Several polynomial algorithms in the literature are proposed for special classes of digraphs, but the complexity of solving this problem in general case is still a challenging open question. We present in this paper an O(n) time algorithm to compute an optimal schedule for the class of bipartite digraphs of depth one.展开更多
This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤn modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study of ring theory, depict ...This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤn modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study of ring theory, depict relationships between elements of a ring that multiply to zero. The paper explores the development and implementation of algorithms in MAPLE for constructing these ZDGs. The comparative study aims to discern the strengths, limitations, and computational efficiency of different MAPLE algorithms for creating zero divisor graphs offering insights for mathematicians, researchers, and computational enthusiasts involved in ring theory and mathematical computations.展开更多
人工智能技术在教育领域的深度应用,已成为国家教育数字化转型的核心战略。在计算机实践教学领域,实践学习资料的精准推荐是提升学生学习效能与质量的重要途径。针对高校教育规模化与学生需求多元化之间的矛盾,提出一种基于轻量级教育...人工智能技术在教育领域的深度应用,已成为国家教育数字化转型的核心战略。在计算机实践教学领域,实践学习资料的精准推荐是提升学生学习效能与质量的重要途径。针对高校教育规模化与学生需求多元化之间的矛盾,提出一种基于轻量级教育大模型的个性化实践学习资料推荐模型LightPLRec(Lightweight Personalized Learning Recommender for Dynamic Practice Materials),旨在依据学生个体特征的动态变化智能推荐个性化的实践学习资料。基于低算力需求的轻量级大模型,通过指令微调和强化学习方法构建了面向个性化实践学习资料推荐的教育大模型SPIR(Student Profile&Interest-based Re-commender)。通过整合多源异构数据,深度融入课程知识体系、学科前沿动态、产业发展趋势、国家战略导向,构建了跨学科、多模态的实践学习资料库,并设计了图转主题文本方法gragh2topic。依托于SPIR大模型的强大赋能和多源资料库的坚实支撑,提出了基于智能工作流的资料推荐方法。设计主题分析方法从学生能力评估结果中提取学生的能力特征,应用图卷积网络算法GCN从学生学习行为数据中挖掘学生的兴趣特征,创建了“能力-推荐智能体”和“兴趣-推荐智能体”,构建了双智能体协同驱动的智能化流程体系,实现了从学生个性化画像智能生成到实践学习资料动态推荐的系列工作流任务;并且构建了个性化资料推荐数据集,在该数据集上验证了所提模型的性能显著优于基线模型。其中,以Qwen2.5-3.0B为基模型训练的LightPLRec模型,在能力推荐与兴趣推荐这两项任务中展现出卓越性能,准确率分别高达0.947和0.939,其表现均优于DeepSeek-V3在同一数据集上的测评结果。该研究为教育大模型的垂直场景应用提供了技术范式,同时通过创建个性化实践学习资料动态推荐模型,为践行“因材施教”理念和培育高素质计算机实践人才提供了创新路径。展开更多
基金supported by the National Key Research and Development Program of China(Grant No.2021YFB0301200)the Hunan Natural Science Foundation Project(Grant No.2023JJ40555)+1 种基金the Hunan Provincial Graduate Student Research and Innovation Project(Grant No.LXBZZ2024035)the Hunan Provincial Department of Education Scientific Research Project(Grant No.22B0451).
摘要GraphX is a graph computing library based on Spark systems,where fault tolerance is a necessary guarantee for the high availability.However,the existing fault tolerance methods are mostly implemented in a pessimistic way and are aimed at general computing tasks.Considering the characteristics of iterative computation,this paper presents a combination method of the optimistic fault tolerance and checkpoint for recovering the data under different failure conditions.Firstly,for single node failure,we propose the optimistic fault tolerance mechanism based on compensation function.It does not add fault tolerance measures in advance and will not incur additional costs when there are no failures.Secondly,for multiple node failures,we propose the automatic checkpoint management strategy based on RDD importance.It comprehensively considers the factors of lineage length of RDD,dependency relationship,and computation time of RDD,which can set the RDD as the checkpoint properly.Finally,we implement our proposals in GraphX of Spark−3.5.1,and evaluate the performance by using representative iterative graph algorithms on the high performance computing cluster.The results verify the correctness of iteration results of the mechanism,and illustrate that when recovering the RDD partition,the job execution time can be reduced by the mechanism and strategy substantially.
摘要In this paper, we derive, by presenting some suitable notations, three typical graph aLgorithms and corresponding programs using a unified approach, partition-and-recur. We putemphasis on the derivation rather than the algorithms themselves. The main ideas and lugesnutty of these algorithms are revealed by formula deduction. Success in these examples givesus more evidence that partition-and-recur is a simple and practical approach and developingenough suitable notations is the key in designing and deriving efficient and correct algorithmicprograms.
基金Supported by the National Natural Science Foundation of China (60970016,61173032)
摘要Hardware/software(HW/SW) partitioning is one of the key processes in an embedded system.It is used to determine which system components are assigned to hardware and which are processed by software.In contrast with previous research that focuses on developing efficient heuristic,we focus on the pre-process of the task graph before the HW/SW partitioning in this paper,that is,enumerating all the sub-graphs that meet the requirements.Experimental results showed that the original graph can be reduced to 67% in the worst-case scenario and 58% in the best-case scenario.In conclusion,the reduced task graph saved hardware area while improving partitioning speed and accuracy.
基金supported by the National Natural Science Foundation of China under Grant No.61372092the China National Science and Technology Major Projects on New Generation Broadband Wireless Mobile Communications Network under Grants No.2011ZX03005-004,No.2012ZX03001029-003,No.2012ZX03001008-003
摘要Femtocell is a promising technology for improving indoor coverage and offloading the macrocell.Femtocells tend to be densely deployed in populated areas such as the dormitories.However,the inter-tier interference seriously exists in the co-channel Densely Deployed Femtocell Network(DDFN).Since the Femtocell Access Points(FAPs) are randomly deployed by their customers,the interference cannot be predicted in advance.Meanwhile,new characteristics such as the short radius of femtocell and the small number of users lead to the inefficiency of the traditional frequency reuse algorithms such as Fractional Frequency Reuse(FFR).Aiming for the downlink interference coordination in the DDFN,in this paper,we propose a User-oriented Graph based Frequency Allocation(UGFA)algorithm.Firstly,we construct the interference graph for users in the network.Secondly,we study the conventional graph based resources allocation algorithm.Then an improved two steps graph based frequency allocation mechanism is proposed.Simulation results show that UGFA has a high frequency reuse ratio mean while guarantees a better throughput.
基金supported by Shandong Provincial Key Research and Development Program of China(2021CXGC010107,2020CXGC010107)the Shandong Provincial Natural Science Foundation of China(ZR2020KF035)the New 20 Project of Higher Education of Jinan,China(202228017).
摘要Blockchain technology,with its attributes of decentralization,immutability,and traceability,has emerged as a powerful catalyst for enhancing traditional industries in terms of optimizing business processes.However,transaction performance and scalability has become the main challenges hindering the widespread adoption of blockchain.Due to its inability to meet the demands of high-frequency trading,blockchain cannot be adopted in many scenarios.To improve the transaction capacity,researchers have proposed some on-chain scaling technologies,including lightning networks,directed acyclic graph technology,state channels,and shardingmechanisms,inwhich sharding emerges as a potential scaling technology.Nevertheless,excessive cross-shard transactions and uneven shard workloads prevent the sharding mechanism from achieving the expected aim.This paper proposes a graphbased sharding scheme for public blockchain to efficiently balance the transaction distribution.Bymitigating crossshard transactions and evening-out workloads among shards,the scheme reduces transaction confirmation latency and enhances the transaction capacity of the blockchain.Therefore,the scheme can achieve a high-frequency transaction as well as a better blockchain scalability.Experiments results show that the scheme effectively reduces the cross-shard transaction ratio to a range of 35%-56%and significantly decreases the transaction confirmation latency to 6 s in a blockchain with no more than 25 shards.
基金Supported by the National Natural Science Foundation of China (601133010)
摘要In this paper, a new approach for visualizing multivariate categorical data is presented. The approach uses a graph to represent multivariate categorical data and draws the graph in such a way that we can identify patterns, trends and relationship within the data. A mathematical model for the graph layout problem is deduced and a spectral graph drawing algorithm for visualizing multivariate categorical data is proposed. The experiments show that the drawings by the algorithm well capture the structures of multivariate categorical data and the computing speed is fast.
摘要To construct a high efficient text clustering algorithm the multilevel graph model and the refinement algorithm used in the uncoarsening phase is discussed. The model is applied to text clustering. The performance of clustering algorithm has to be improved with the refinement algorithm application. The experiment result demonstrated that the multilevel graph text clustering algorithm is available. Key words text clustering - multilevel coarsen graph model - refinement algorithm - high-dimensional clustering CLC number TP301 Foundation item: Supported by the National Natural Science Foundation of China (60173051)Biography: CHEN Jian-bin(1970-), male, Associate professor, Ph. D., research direction: data mining.
基金supported by the National Science Foundation for Distinguished Young Scholars of China(Grant Nos.61003082 and 60903059)the National Natural Science Foundation of China(Grant No.60873014)the Foundation for Innovative Research Groups of the National Natural Science Foundation of China(Grant No.60921062)
摘要Many real-world networks are found to be scale-free. However, graph partition technology, as a technology capable of parallel computing, performs poorly when scale-free graphs are provided. The reason for this is that traditional partitioning algorithms are designed for random networks and regular networks, rather than for scale-free networks. Multilevel graph-partitioning algorithms are currently considered to be the state of the art and are used extensively. In this paper, we analyse the reasons why traditional multilevel graph-partitioning algorithms perform poorly and present a new multilevel graph-partitioning paradigm, top down partitioning, which derives its name from the comparison with the traditional bottom-up partitioning. A new multilevel partitioning algorithm, named betweenness-based partitioning algorithm, is also presented as an implementation of top-down partitioning paradigm. An experimental evaluation of seven different real-world scale-free networks shows that the betweenness-based partitioning algorithm significantly outperforms the existing state-of-the-art approaches.
摘要电力系统的安全稳定运行是保障国家能源安全和经济发展的关键,而这在很大程度上依赖于对电力物联设备故障的准确预测。当前,随着电力物联网技术的发展,大量的数据被采集,但这些数据的潜在价值尚未得到充分挖掘,这在一定程度上限制了故障预测的准确性,影响了电力系统的可靠运行。针对这一问题,该文提出了一种创新的基于GraphSAGE(Graph Sample and Aggregate)算法的电力物联设备故障预测。该方法通过PowerGraph数据集,将电力物联设备故障场景细分为四类,利用GraphSAGE模型的特性,深入学习和分析节点特征与边特征,从而实现对物联设备故障的有效预测。实验结果表明,该方法准确率达到97.5%,相较于其它传统方法,准确率提高了0.39%~6.21%,同时GraphSAGE模型实现了快速训练。该方法为电力物联设备安全稳定运行提供重要决策支持,能够对动态和相互联系的复杂系统进行更精细的分析,并增强电力系统运营部门对潜在干扰的预见和应对能力。
基金Supported by the National Natural Science Foundation of China(Grant No.11271365)the Domestic Senior Visiting Scholar Program in Higher Occupation Colleges in Jiangsu Province(Grant No.2014FX075)
摘要The 2-step domination problem is to find a minimum vertex set D of a graph such that every vertex of the graph is either in D or at distance two from some vertex of D. In the present paper, by using a labeling method, we provide an O(m) time algorithm to solve the 2-step domination problem on block graphs, a superclass of trees.
摘要It is a common practice to simulate some historical or test systems to validate the efficiency of new methods or concepts. However, there are only a small number of existing power system test cases, and validation and evaluation results, obtained using such a limited number of test cases, may not be deemed sufficient or convincing. In order to provide more available test cases, a new random graph generation algorithm, named ‘‘dualstage constructed random graph’’ algorithm, is proposed to effectively model the power grid topology. The algorithm generates a spanning tree to guarantee the connectivity of random graphs and is capable of controlling the number of lines precisely. No matter how much the average degree is,whether sparse or not, random graphs can be quickly formed to satisfy the requirements. An approach is developed to generate random graphs with prescribed numbers of connected components, in order to simulate the power grid topology under fault conditions. Our experimental study on several realistic power grid topologies proves that the proposed algorithm can quickly generate a large number of random graphs with the topology characteristics of real-world power grid.
摘要Optical transport networks are now the basic infrastructure of modern communications systems, including the SDH and WDM backbone network of local network operators, in the case of Cameroon. Given the colossal investments required to deploy these networks, particularly related to the cost of equipment (optical fibers, transponders and multiplexers), the optimization of bandwidth and dynamic allocation of resources is essential to control operating costs and ensure continuity of service. Automatic switching technology for optical networks brings intelligence to the control plane to fully facilitate bandwidth utilization, traffic redirection, and automatic configuration of end-to-end services. This paper considers a local network operator’s WDM network without the implementation of the automatic switching technology, develops a network modeling software platform called Graphic Networks and using graph theory integrates a particularity of the automatic switching technology, which is the automatic rerouting of traffic in case of incident in the network. The incidents considered here are those links or route failures and node failures.
摘要Given n unit execution time (UET) tasks whose precedence constraints form a directed acyclic graph, the arcs are associated with unit communication time (UCT) delays. The problem is to schedule the tasks on two identical processors in order to minimize the makespan. Several polynomial algorithms in the literature are proposed for special classes of digraphs, but the complexity of solving this problem in general case is still a challenging open question. We present in this paper an O(n) time algorithm to compute an optimal schedule for the class of bipartite digraphs of depth one.
摘要This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤn modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study of ring theory, depict relationships between elements of a ring that multiply to zero. The paper explores the development and implementation of algorithms in MAPLE for constructing these ZDGs. The comparative study aims to discern the strengths, limitations, and computational efficiency of different MAPLE algorithms for creating zero divisor graphs offering insights for mathematicians, researchers, and computational enthusiasts involved in ring theory and mathematical computations.
摘要人工智能技术在教育领域的深度应用,已成为国家教育数字化转型的核心战略。在计算机实践教学领域,实践学习资料的精准推荐是提升学生学习效能与质量的重要途径。针对高校教育规模化与学生需求多元化之间的矛盾,提出一种基于轻量级教育大模型的个性化实践学习资料推荐模型LightPLRec(Lightweight Personalized Learning Recommender for Dynamic Practice Materials),旨在依据学生个体特征的动态变化智能推荐个性化的实践学习资料。基于低算力需求的轻量级大模型,通过指令微调和强化学习方法构建了面向个性化实践学习资料推荐的教育大模型SPIR(Student Profile&Interest-based Re-commender)。通过整合多源异构数据,深度融入课程知识体系、学科前沿动态、产业发展趋势、国家战略导向,构建了跨学科、多模态的实践学习资料库,并设计了图转主题文本方法gragh2topic。依托于SPIR大模型的强大赋能和多源资料库的坚实支撑,提出了基于智能工作流的资料推荐方法。设计主题分析方法从学生能力评估结果中提取学生的能力特征,应用图卷积网络算法GCN从学生学习行为数据中挖掘学生的兴趣特征,创建了“能力-推荐智能体”和“兴趣-推荐智能体”,构建了双智能体协同驱动的智能化流程体系,实现了从学生个性化画像智能生成到实践学习资料动态推荐的系列工作流任务;并且构建了个性化资料推荐数据集,在该数据集上验证了所提模型的性能显著优于基线模型。其中,以Qwen2.5-3.0B为基模型训练的LightPLRec模型,在能力推荐与兴趣推荐这两项任务中展现出卓越性能,准确率分别高达0.947和0.939,其表现均优于DeepSeek-V3在同一数据集上的测评结果。该研究为教育大模型的垂直场景应用提供了技术范式,同时通过创建个性化实践学习资料动态推荐模型,为践行“因材施教”理念和培育高素质计算机实践人才提供了创新路径。